An automatically operating core drilling unit of above mentioned type is described in PCT/SE2005/000472. Similar units are produced and marketed by the Dimas company, associated with the applicant, under the brand name Dimas DS40/50 Gyro and is also described in Dimas' brochures, see also www.dimas.com. By means of these and other core drilling units, it is possible to drill vertically in ceilings as well. Water is hereby, according to prior art, fed into the cylindrical cavity in the core drill via a duct that extends through the machine shaft, ending at the bottom of the cylinder formed by the core drill, so that the core drill is fully filled by cooling liquid. During drilling, the water is pressed upwards through the circular drilling cut that is formed in the ceiling, after which the water including the drill cuttings will flow downwards along the outside surface of the drill. Measures must consequently be taken to prevent water from flowing down onto the drilling machine underneath the drill, otherwise there is a risk of short-circuiting the drilling motor and/or other damage occurring in the machine. However, there are no good devices available to collect and divert the water, so that it does not come in contact with the drilling machine. Lacking better solutions, it is therefore common practice to cover the drilling machine including the drilling motor with plastic film. This is however troublesome and does not in any case constitute a reliable solution to the problem of protecting the drilling machine including the drilling motor from water damage. Besides, the cooling water with the drill cuttings from the plastic foil covering flows down onto the floor, from where it has to be removed in some way. It can be understood that core drilling in ceilings therefore constitutes a dirty and from many aspects unpleasant task.